Monks - Audioplimization Goal-Based Acoustic Design, dokumenty, Akustyka
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Feature Article
Audioptimization:
Goal-Based
Acoustic Design
Michael Monks, Byong Mok Oh, and Julie Dorsey
Massachusetts Institute of Technology
human perception of sound depends on
such things as decibel level, direction of propagation, and
attenuation over time—none of which are tangible or vis-
ible. Traditionally, designers have built physical scale
models and tested them visually and acoustically. For
example, by coating the interiors of the models with
reflective material and then shining lasers from various
source positions, they assess the sight and sound lines of
the audience in a hall. They also
might attempt to measure acoustical
qualities of a proposed environment
by conducting acoustic tests on the
model using sources and receivers
scaled in both frequency and size.
Even water models are used some-
times to visualize the acoustic wave
propagation in a design. These tradi-
tional methods have proven inflexi-
ble, costly, and time-consuming to
implement, and they have created
some major acoustic failures.
1
The advent of computer simula-
tion and visualization techniques for acoustic design and
analysis has yielded a variety of approaches for model-
ing acoustic performance.
2-4
Research in this area to date
has mainly addressed the accuracy and speed of the sim-
ulation algorithms and offered effective visualizations
or auralizations of the resulting multidimensional data.
However, while these techniques certainly offer new
insights into acoustic design, they fail to enhance the
design process itself, which still involves a burdensome
iterative process of trial and error.
Many complex, often-conflicting goals and constraints
generally mark the design process. For instance, financial
concerns might dictate a larger hall with increased seat-
ing capacity. This can have negative effects on the hall’s
acoustics, such as excessive reverberation and noticeable
gaps between direct and reverberant sound. Fan-shaped
halls bring the audience closer to the stage than other
configurations, but they may fail to make the listener feel
surrounded by the sound. The application of highly
A
coustic design is difficult because the
absorbent materials may reduce disturbing echoes, but
they may also deaden the hall.
In many renovations, budgetary, aesthetic, or physi-
cal impediments limit modifications, compounding the
difficulties confronting the designer. In addition, a hall
might need to accommodate a wide range of perfor-
mances, from lectures to symphonic music, each with
different acoustic requirements. In short, a concert hall’s
acoustics depends on the designer’s ability to balance
many factors.
Here, we present an inverse, interactive acoustic
design approach that helps a designer produce an archi-
tectural configuration that achieves a desired acoustic
performance. For a new building, the system may sug-
gest optimal configurations that would not otherwise
be considered; for a hall with modifiable components
or for a renovation project, it may assist in optimizing
an existing configuration. Our system allows the design-
er to constrain changes to the environment and specify
acoustic performance goals as a function of time. The
constraints include the specification of a range of allow-
able materials as well as geometric modifications for sur-
faces in the hall. The designer also specifies goals for
acoustic performance in space and time via high-level
acoustic qualities such as decay time and sound level.
Using this information, the system performs a con-
strained optimization of surface material and geometric
parameters for a subset of elements in the environment.
The system operates at varying accuracy levels, offer-
ing trade-offs between time and quality. Visualization
tools facilitate an intuitive assessment of the complex
time-dependent nature of sound, and they provide a
means to express desired performance. By using opti-
mization routines within an interactive application, our
system reveals complex acoustic properties and steers
the design process toward the designer’s goals.
We present a new inverse,
interactive approach to
acoustic design that applies
optimization techniques to
an acoustic simulation
system.
Background
Our approach synthesizes and extends previous
research in the areas of interactive design and opti-
mization, acoustic simulation and visualization, and
characterization of sound.
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May/June 2000
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Interactive design, optimization techniques
Today’s CAD systems for lighting, acoustic, and other
types of simulation-intensive design are based almost
exclusively on direct methods: those that compute a
solution from a complete description of an environment
and relevant parameters. Such systems can be extreme-
ly useful in evaluating the performance of a given 3D
environment. However, they involve a tedious specify-
simulate-evaluate loop in which users are responsible
for specifying input parameters and for evaluating the
results. The computer is responsible only for comput-
ing and displaying the results of these simulations. The
drawback of this method is especially noticeable if a
costly simulation (for example, lighting or acoustic) is
part of the loop. This makes interactive searching of the
design space impossible.
Recently, Marks et al. developed a methodology,
called design galleries, for searching large parameter
spaces typical of design problems.
5
The system auto-
matically generates a palette of widely spaced, distinct
choices from which users may select the most appro-
priate one. While this technique allows users to explore
a variety of different configurations, it is less useful in
problems—such as acoustic design—for which the
goals are known in advance or that have a large num-
ber of degrees of freedom.
An alternative approach to design considers the
inverse problem—that is, allowing users to create a tar-
get and have the algorithm work backward to establish
various parameters. In this division of labor, users must
now specify objectives to achieve in a scene. The com-
puter searches the design space, that is, it selects para-
meters optimally with respect to user-supplied
objectives. Several lighting design and rendering sys-
tems have employed inverse design. For example, users
can specify the location of highlights and shadows,
6
pixel intensities or surface radiance values,
7
or subjec-
tive impressions of illumination.
8
The computer then
attempts to determine lighting or reflectance parame-
ters that best match the given objectives using opti-
mization techniques. Because sound is considerably
more complex than light, an inverse approach appears
to have even more potential in assisting acoustic design-
ers. We build on previous inverse design systems by
optimizing not only over materials but also over geo-
metric parameters.
The role of optimization in a design system is to find
the configuration in the feasible design space that best
matches desired performance goals. The choice of an
optimization technique depends on the nature of the
design space and the types of constraints. Here, we for-
mulate the acoustic design problem as a constrained,
nonlinear optimization problem. The basic constrained
optimization problem is to minimize the scalar quanti-
ty of an objective function of
n
system parameters while
satisfying a set of constraints. Standard nonlinear opti-
mization techniques use the gradient and curvature of
the objective function to descend to a minimum or
locally optimal configuration.
9
Our evaluation func-
tions have multiple such minima and therefore require
a global strategy. Hence, we first employ a global opti-
mization technique—simulated annealing—to locate
The role of optimization in a design system
is to find the configuration in the feasible
design space that best matches desired
performance goals. The choice of an
optimization technique depends on the
nature of the design space and
the types of constraints.
a more globally optimal neighborhood. We then use the
steepest descent algorithm to descend to the minimum.
Acoustic simulation and visualization
Previous work in acoustic simulation
1
can be divided
into five general categories: image source methods,
2
radiant exchange methods,
3,10
statistical methods, ray
tracing,
11
and beam tracing.
3,12,13
A variety of hybrid sim-
ulation techniques typically approximate the sound field
by modeling the early and late sound fields separately
and combining the results.
3
We employ such a hybrid simulation engine, which
models the early sound with beam tracing and the late
sound with a statistical approximation.
14
With this sim-
ulation approach, a receiver-independent preprocess-
ing step determines the location of all virtual sources up
to a specified reflection depth and calculates the sub-
volume of the room that each virtual source influences.
The late sound is modeled by a statistical tail, a single
source distributing the remaining energy to all locations
equally as it decays. Once a receiver location is speci-
fied, we determine a list of valid virtual sources, each
contributing sound energy to that receiver in the form
of a discrete arrival. We can then calculate acoustic mea-
sures using the list of discrete arrivals and the precal-
culated statistical tail.
The simulation engine has several characteristics rel-
evant to our work. First, since the geometric prepro-
cessing step is independent of location and time, we can
specify a receiver location at any stage of design and
obtain its set of acoustic data merely by sampling the
precalculated sound field. Second, the cost of modify-
ing surface materials in the hall is a small fraction of that
of modifying geometry. Changes in geometry invalidate
a portion of the beam tree data structure and therefore
require its reconstruction, while changes in materials
require only that the energy contributions of affected
beams be updated. Finally, it’s possible to trade quality
for speed by reducing the reflection depth of the beam
tracing, culling beams with minimal contribution,
and/or reducing sampling density. An important
attribute of our system is that it can be used in conjunc-
tion with virtually any acoustic simulation algorithm.
Other work has been done in representing sound field
IEEE Computer Graphics and Applications
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Feature Article
θ
IACC, shown in Figure 1, is a shell
located on the sides of each listener
icon. The greater the degree of
encirclement of the icon by the shell,
the more desirable is the IACC value.
r
1
Glyphs repre-
senting (a)
IACC, (b) early
decay time
(EDT), and (c)
bass ratio (BR).
0 1.0 2.
0
Mid
Early decay time. EDT mea-
sures the reverberation or liveliness
of a hall. Musicians characterize a
hall as “dead” or “live,” depending
on whether EDT is too low or high.
The formal definition of EDT is the
time it takes for the level of sound
to drop 10 decibels from its initial
level, which is then normalized for
comparison to traditional measures of reverberation by
multiplying the value by six. As Beranek suggests, we
determine EDT by averaging the values of EDT for 500-
Hz and 1,000-Hz sound pulses. The best values of EDT
range between 2.0 and 2.3 seconds for concert halls.
The icon we use to portray EDT at a receiver position is
a cone in which the height is fixed and the radius is
scaled according to the decay time (see Figure 1). For
a value of 2.0 seconds, the cone is twice the width of
the listener icon.
Low
IACC =
θ
180
°
EDT = r
BR =
low
mid
(a)
(b)
(c)
data with visualizations and auralizations. Stettner and
Greenberg presented a set of 3D glyphs to convey graph-
ically the behavior of sound within an enclosure.
15
The
Bose Auditioner system provides auralizations from sim-
ulation data at listener positions within a modeled hall.
4
These auralizations approximate what the hall might
sound like. Our system provides visualizations for a col-
lection of acoustic measures that describe the character
of the sound field as it varies in space and time within an
environment. We use these visualizations both to ana-
lyze the behavior of a given design and to specify desir-
able performance goals interactively.
Bass ratio. BR measures how much sound comes
from bass, reflecting the persistence of low-frequency
energy relative to mid-frequency energy. Musicians refer
to BR as the “warmth” of the sound. BR is defined as
Characterization of sound
Traditionally, reverberation time and other early
decay measurements were considered the primary eval-
uation parameters in acoustic design. However, in recent
years, researchers have recognized the inadequacies of
using these criteria alone and have introduced a variety
of additional measures aimed at characterizing the sub-
jective impression of human listeners.
1
In 1996 Beranek
introduced an evaluation function that gives an overall
acoustic rating by linearly combining six statistically
independent objective acoustic measures.
16
This func-
tion builds on the work of Ando.
17
We employ Beranek’s
evaluation approach, known as the Objective Rating
Method (ORM). We define the six acoustic measures
and introduce visualization techniques used to evalu-
ate them.
BR
=
RT RT
RT RT
+
+
250
500
1000
RT
f
is the frequency dependent reverberation time at
an octave band centered at frequency
f
.
RT
is the time it
takes for the sound level to drop from 5 dB to 35 dB
below the initial level, which is then normalized for com-
parison to traditional measures of reverberation by mul-
tiplying by two. For example, for a 100-dB initial sound
level,
RT
would be the time it takes to drop from 95 dB
to 65 dB multiplied by the normalizing factor. The ideal
value of
BR
ranges between 1.1 and 1.4 for concert halls.
The graphical icon we use to represent BR at a receiv-
er position consists of a pair of stacked, concentric cylin-
ders of slightly different widths (see Figure 1). The top
cylinder represents the mid-frequency energy, from the
500-Hz and 1,000-Hz bands, and the bottom cylinder
represents the lower frequency energy, from the 125-
Hz and 250-Hz bands. The height of each cylinder rep-
resents the relative values in the ratio, assuming a
constant combined height. A listener icon representing
a desirable BR value of 1.25 would have the top of the
lower cylinder just above the halfway mark, as shown
in Figure 1. Like the other measures discussed so far, BR
varies spatially throughout a hall.
Interaural cross-correlation coefficient. IACC
is a binaural measure of the correlation between the sig-
nals at the two ears of a listener. It characterizes how
surrounded a listener feels by the sound within a hall. If
the sound comes from directly in front of or behind the
listener, it will arrive at both ears at the same time with
complete correlation, producing no stereo effect. If it
comes from another direction, the two signals will be
out of phase and less correlated, giving the listener the
desirable sensation of being enveloped by the sound.
17
The correlation values depend on the arrival direction
of the wave with respect to the listener’s orientation.
Since the amplitude of sound decreases rapidly as it
propagates, the sound waves that arrive the earliest gen-
erally have far greater effect on IACC.
We use a cylinder to represent a receiver in a perfor-
mance space. The graphical icon we use to represent
Strength factor (G). This factor measures sound
level, approximating a general perception of loudness
of the sound in a space. For a given location within the
hall, G is the ratio of the sound energy arriving at that
location from a nondirectional source to the direct
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May/June 2000
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(a)
(b)
2
Color indi-
cates sound
strength data
on room sur-
faces, calculated
for different
integration
intervals:
(a) 10 ms,
(b) 40 ms,
(c) 80 ms, and
(d) 120 ms.
(c)
(d)
sound energy measured at a distance of 10 meters from
the same source. By using this ratio, the influence of
source power is removed from the loudness calculation,
allowing easy comparison of measured data across dif-
ferent halls. We average the values of G at 500 Hz and
1,000 Hz. The preferred values for G range between 4.0
dB and 5.5 dB for concert halls. In general, G is higher
at locations closer to the source.
It is instructive to see how the sound level changes
through time, as well as location. We perceive a reflect-
ed wave front as an echo—perceptibly separable from
the initial sound—if it arrives more than 50 ms after the
direct sound and if it is substantially stronger than its
neighbors. The time distribution of sound also affects
our perception of clarity. Two locations in a hall may
have the same value of G, but if the energy arrives later
with respect to the direct sound for one location than
the other, speech will be less intelligible and music less
crisp. We use color to indicate relative scalar values of
the sound-level data, which is sampled at a fine mesh of
points on surfaces as a function of time. By adjusting a
slider, we can examine the accumulated sound-level
data as a function of space and time. Figure 2 illustrates
a representative time sequence.
parisons among different halls, we record only a single
value per hall, measured at a representative location in
the center of the main seating area. It is best if TI does
not exceed 20 ms.
Surface diffusivity index. SDI is a measure of
the amount of sound diffusion caused by gross surface
detail, or macroscopic roughness of surfaces within a
hall. SDI is usually determined by inspection, and it
correlates to the tonal quality of the sound in a hall.
We compute the SDI index for the entire hall by sum-
ming the SDI assigned to each surface material,
weighted by its area with respect to the total surface
area of the hall. SDI can range between 0.0 and 1.0,
with larger values representing more diffusion. The
preferred value of SDI is 1.0. For example, plaster has
a lower index than brick, which has a lower index than
corrugated metal.
These six statistically orthogonal acoustic measures
16
form the basis for our analysis and optimization work.
While two of the measures, SDI and TI, are single val-
ues representing the entire hall, we compute the others
by averaging the values sampled at multiple spatial posi-
tions and, in the case of G, multiple points in time.
Initial-time-delay gap (TI). This gap measures
how large the hall sounds, quantifying the perception
of intimacy the listener feels in a space. It depends pure-
ly on the hall’s geometry, measuring the time delay
between the arrival of the direct sound and that of the
first reflected wave to reach the listener. To make com-
Inverse problem formulation
We phrase this problem more formally as follows: given
a description of a set of desired measures for acoustic per-
formance, determine the material properties and geo-
metric configuration that will most closely match the
target. To formulate the acoustic design process as a con-
IEEE Computer Graphics and Applications
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Feature Article
strained optimization problem, we require a specification
of (1) the optimization variables that express how a hall
may be modified, (2) the constraints that must be satis-
fied, and (3) the objective function.
Objective function
Acoustic design problems are typically undercon-
strained. Hence, an infinite number of possible solutions
may exist that satisfy the constraints. An objective or cost
function is necessary to select the optimal configuration
from among the set of feasible solutions. We use Beranek’s
ORM as our objective function, which is an application
of Ando’s Theory of Subjective Preference.
16,17
Ando found
that when
m
orthogonal objective acoustic measures are
given, the following definition of a cost function provides
an
a
cceptable scalar rating of a hall:
Optimization variables
In a typical acoustic simulation system, the goal is to
compute the sound field in a scene assuming a sound
source and a description of the geometry and materials.
The measures just described are the unknowns, which
are computed in terms of static material properties and
geometry. In the optimization problem, material and
geometric properties are no longer fixed but are treated
as variables.
A hall consists of a collection of polygons, subsets of
which may be grouped into geometric components.
Components are a convenient and natural way to rep-
resent entities such as balconies, reflectors, and so on.
Each component can have associated with it a set of
allowable linear geometric transformations and a set of
acceptable materials. Each translation, rotation, or scal-
ing of a component represents a geometry variable; a
set of possible materials associated with a component
is a material variable.
m
∑
1
fx w
ii
i
()
=
(1)
=
Here, multidimensional vector
x
represents the con-
figuration of the hall, function
f
i
penalizes the deviation
from the target value of each objective acoustic mea-
sure, and weight
w
i
normalizes the respective functions.
Beranek uses the six objective acoustic measures
(IACC, EDT, BR, G, TI, and SDI) and provides values for
their weights, suitable for symphonic music.
Finally, we minimize the objective function given by
Equation 1 to find the hall configuration that best match-
es the target objective acoustic measures. Note that
objectives may be constructed from all or a subset of the
terms. In addition, it’s possible to build objectives to han-
dle multiple performance types simultaneously, such as
symphonic music and opera. To accomplish this, we lin-
early combine individual objectives as follows:
Constraints
There are two types of constraints. Geometry con-
straints are user-specified upper and lower bounds
placed on each component’s transformation. Each trans-
formation variable represents a single degree of free-
dom: translation along a vector, rotation about a vector,
or scaling about a point or along a vector. The allowable
range of each transformation constraint requires the
component to remain within the specified bounds. For
example,
T
low
≤
f
combined
() () ()
x a f x a f x a f x
=
1
use
1
+
2
use
2
+
L
n use
n
()
T
high
requires the transformation
i
to remain within the bounds of
T
low
and
T
high
.
Material constraints are user-specified sets of allow-
able materials assigned to a given component. This sub-
set of materials is selected from a library of materials
provided by the system. For example, {
plaster,con-
crete,fiberglass
} is a set of materials for a component.
The library is built such that all material properties are
physically sensible.
T
i
≤
Here,
a
i
is the weighting factor of the
i
th individual
objective function given
n
objectives, and the sum of the
weighting factors is 1.0. Note that the minimum cost of
a multiple-use objective function is typically not zero,
since we cannot perfectly achieve all objectives.
Optimization problem
We state this problem as follows: minimize
f
(
x
) subject
to
x
∈
Acoustic simulation
Steepest descent
Simulated annealing
3
Overview of
the interactive
design process.
Optimization
Constraint specification
Target specification
Hall configuration
Acoustic parameters
Establish
constraints and
objectives
Display results
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May/June 2000
X
, where constraint set
X
is the “design space”
spanned by feasible hall configurations. The existence of
constraints implies that not every target is realizable. We
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